Heat oven to 350 degrees F.
Peel outer papery skin from head of garlic. Cut about 1/2-inch slice from top of the head of garlic and discard. Brush cut surface on top of the head with 1 tablespoon of the olive oil. Wrap the head in aluminum foil.
Roast garlic in 350 degree F oven for 1 hour or until softened.
In large pot, combine rutabaga with enough cold water to cover by 1 inch. Add 1/2 teaspoon of the salt. Bring to a boil over high heat. Reduce heat to medium-high; simmer for 40 to 45 minutes or until the rutabaga is fork-tender. Drain; return the rutabaga to pot and keep warm.
Meanwhile, in a second large pot, combine potatoes with enough cold water to cover by 1 inch. Add 1/2 teaspoon of the salt. Bring to a boil over high heat. Reduce the heat to medium; simmer for 25 to 30 minutes or until fork-tender. Drain; add the potatoes to the rutabaga in the pot; keep warm.
In medium-size skillet, heat the remaining 1 tablespoon oil over medium-high heat. Add onion; saute, stirring frequently, for 5 minutes or until lightly browned.
Add the onion to the rutabaga mixture in the pot. Squeeze garlic pulp from the skins into the rutabaga mixture. Mash all the ingredients together to combine. Add the remaining 1-1/2 teaspoons salt, the butter and black pepper. Mash until the mixture is as smooth as desired. Stir in thyme. Makes 8 servings.